package h0907;

/**
 * @author 不知名帅哥
 * @version 1.0
 * @description 最小路径和
 * @date 2024/9/7 23:01
 */
public class SmallestPathSum {
    public static void main(String[] args) {
        int[][] arr={
                {1,3,1},
                {1,5,1},
                {4,2,1}
        };
        System.out.println(minPathSum(arr));
    }

    public static int minPathSum(int[][] grid) {

        int m = grid.length;
        int n = grid[0].length;
        int[][] dp = new int[m][n];
        //初始化
        //第一行
        dp[0][0] = grid[0][0];
        for (int i = 1; i < n; i++) {
            dp[0][i] = dp[0][i - 1] + grid[0][i];
        }
        //第一列
        for (int i = 1; i < m; i++) {
            dp[i][0] = dp[i - 1][0] + grid[i][0];
        }

        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                dp[i][j] = Math.min(dp[i - 1][j] + grid[i][j], dp[i][j - 1] + grid[i][j]);
            }
        }
        return dp[m-1][n-1];
    }
}
